To pass the whole word e.g. keyword or 0, replace on_text with on_text_validate.

DRY - Don't Repeat Yourselves

There are duplicate codes, I have turned them into modules for easy maintenance.

def create_treeview_root(self):
...
def create_treeview_branch(self, obj):
...
def dismiss_callback(self):

Snippet

GroupScreen:
    ...
        SingleLineTextInput:
            id: name
            focus: True
            multiline: False
            on_text_validate: root.display_groups(self)

Example

main.py

from kivy.uix.screenmanager import Screen
from kivy.app import App
from kivy.lang import Builder
from kivy.core.window import Window
from kivy.uix.popup import Popup
from kivy.uix.treeview import TreeView, TreeViewLabel, TreeViewNode
from kivy.uix.label import Label
from kivy.properties import ObjectProperty, StringProperty, ListProperty
Window.size = (500, 400)


def populate_tree_view(tree_view, parent, node):
    if parent is None:
        tree_node = tree_view.add_node(TreeViewLabel(text=node['node_id'],
                                                     is_open=True))
    else:
        tree_node = tree_view.add_node(TreeViewLabel(text=node['node_id'],
                                                     is_open=True), parent)

    for child_node in node['children']:
        populate_tree_view(tree_view, tree_node, child_node)


class TreeViewLabel(Label, TreeViewNode):
    pass


class TreeviewGroup(Popup):
    treeview = ObjectProperty(None)
    tv = ObjectProperty(None)
    filter_text = StringProperty('')
    tree = ListProperty([])

    def __init__(self, obj, **kwargs):
        super(TreeviewGroup, self).__init__(**kwargs)
        self.create_treeview_root()
        rows = [('test{}').format(i) for i in range(1, 20)]
        self.tree = [{'node_id': r, 'children': []} for r in rows]
        self.tv.bind(minimum_height=self.treeview.setter('height'))
        self.create_treeview_branch(self.tree)

    def create_treeview_root(self):
        self.tv = TreeView(root_options=dict(text=""),
                           hide_root=False,
                           indent_level=4)

    def create_treeview_branch(self, obj):
        for branch in obj:
            populate_tree_view(self.tv, None, branch)
        self.treeview.add_widget(self.tv)

    def on_open(self):
        self.filter_text = App.get_running_app().root.name.text

    def dismiss_callback(self):
        self.treeview.clear_widgets()
        self.dismiss()
        App.get_running_app().root.name.focus = True

    def filter(self, f):
        self.treeview.clear_widgets()
        self.create_treeview_root()
        new_tree = []
        for n in self.tree:
            if f.lower() in n['node_id'].lower():
                new_tree.append(n)
        self.create_treeview_branch(new_tree)


class GroupScreen(Screen):
    name = ObjectProperty(None)
    popup = ObjectProperty(None)

    def display_groups(self, instance):
        if len(instance.text) > 0:
            if self.popup is None:
                self.popup = TreeviewGroup(self)
            self.popup.open()


class Group(App):
    def build(self):
        self.root = Builder.load_file('test.kv')
        return self.root


if __name__ == '__main__':
    Group().run()

test.kv

#:kivy 1.10.0

<TreeViewLabel>:
    on_touch_down:
        app.root.name.text = self.text
        app.root.popup.dismiss_callback()

<TreeviewGroup>:
    treeview: treeview
    title: "Select"
    title_size: 17
    size: 800, 800
    auto_dismiss: False
    scroll: scroll
    fltr : fltr

    BoxLayout
        orientation: "vertical"
        TextInput:
            id : fltr
            focus: True
            text: root.filter_text
            size_hint_y: .13
            on_text: root.filter(self.text)

        ScrollView:
            id: scroll
            size_hint: 1, .9


            BoxLayout:
                size_hint_y: None
                id: treeview

        GridLayout:
            cols: 2
            row_default_height: '20dp'
            size_hint: .5, 0.1
            pos_hint: {'x': .25, 'y': 1}
            Button:
                text: 'Ok'
                on_release:
                    root.dismiss_callback()

            Button:
                text: 'Cancel'
                on_release:
                    root.dismiss_callback()

<CustomLabel@Label>:
    text_size: self.size
    valign: "middle"
    padding_x: 5

<SingleLineTextInput@TextInput>:
    multiline: False

<GreenButton@Button>:
    background_color: 1, 1, 1, 1
    size_hint_y: None
    height: self.parent.height * 0.150

GroupScreen:
    name: name

    GridLayout:
        cols: 2
        padding : 30,30
        spacing: 10, 10
        row_default_height: '40dp'

        CustomLabel:
            text: ' '

        CustomLabel:
            text: ' '

        CustomLabel:
            text: 'Name'

        SingleLineTextInput:
            id: name
            focus: True
            multiline: False
            on_text_validate: root.display_groups(self)

        GreenButton:
            text: 'Ok'

        GreenButton:
            text: 'Cancel'
            on_press: app.stop()

Output